It is customary to talk about the regression of Y on X, so that if we were predicting GPA from SAT we would talk about the regression of GPA on SAT. The X variable is often called the predictor and Y is often called the criterion (the plural of 'criterion' is 'criteria'). It is customary to call the independent variable X and the dependent variable Y. The linear model assumes that the relations between two variables can be summarized by a straight line. Why does testing for the regression sum of squares turn out to have the same result as testing for R-square? What does it mean to test the significance of the regression sum of squares? R-square? How do we find the slope and intercept for the regression line with a single independent variable? (Either formula for the slope is acceptable.) What does it mean to choose a regression line to satisfy the loss function of least squares? How do changes in the slope and intercept affect (move) the regression line? ![]() If the scatter plot reveals non linear relationship, often a suitable transformation can be used to attain linearity.According to the regression (linear) model, what are the two parts of variance of the dependent variable? (Write an equation and state in your own words what this says.) One can construct the scatter plot to confirm this assumption. It finds the slope and the intercept assuming that the relationship between the independent and dependent variable can be best explained by a straight line. Linear regression does not test whether data is linear. Statistically, it is equivalent to testing the null hypothesis that the regression coefficient is zero. A related question is whether the independent variable significantly influences the dependent variable. The closer R2 is to 1, the better is the model and its prediction. All software provides it whenever regression procedure is run. Once a line of regression has been constructed, one can check how good it is (in terms of predictive ability) by examining the coefficient of determination (R2). A similar interpretation can be given for the regression coefficient of X on Y. It represents change in the value of dependent variable (Y) corresponding to unit change in the value of independent variable (X).įor instance if the regression coefficient of Y on X is 0.53 units, it would indicate that Y will increase by 0.53 if X increased by 1 unit. The coefficient of X in the line of regression of Y on X is called the regression coefficient of Y on X. We would then be able to estimate crop yield given rainfall.Ĭareless use of linear regression analysis could mean construction of regression line of X on Y which would demonstrate the laughable scenario that rainfall is dependent on crop yield this would suggest that if you grow really big crops you will be guaranteed a heavy rainfall. Here construction of regression line of Y on X would make sense and would be able to demonstrate the dependence of crop yield on rainfall. ![]() ![]() Choice of Line of Regressionįor example, consider two variables crop yield (Y) and rainfall (X). Often, only one of these lines make sense.Įxactly which of these will be appropriate for the analysis in hand will depend on labeling of dependent and independent variable in the problem to be analyzed. On the other hand, the line of regression of X on Y is given by X = c + dY which is used to predict the unknown value of variable X using the known value of variable Y. This is used to predict the unknown value of variable Y when value of variable X is known. The line of regression of Y on X is given by Y = a + bX where a and b are unknown constants known as intercept and slope of the equation. There are two lines of regression- that of Y on X and X on Y.
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